Stress crack tip

Crack Tip Stresses. The simplest case for fracture mechanics analysis is a linear elastic material where stress. O, is proportional to strain, S,... 

Fracture Toughness. The fracture criterion was defined by a critical value of the crack tip stress intensity, known as the fracture toughness. Ceramics often fail ia pure tension, designated mode I, and Kj replaces ia equation 6. Thus die appHed tensile stress at which fracture... 

Under some citcumstances the crack tip stress intensity is different than far-field stresses would indicate because of microstmctural effects behind the crack tip, such as fibers, whiskers, and bridging grains. Often far-field values indicate the crack is propagating at a stress intensity value higher than Kj and this apparent value usually increases as crack length increases. In spite of indications to the contrary, bonds continue to break at the same value of the stress intensity however, the crack tip is being shielded from some of the appHed stress intensity. To minimize confusion about Kj it has been suggested that the farfield value of the stress intensity be called When there are no microstmctural features that effectively reduce the crack tip stress intensity,... 

Linear elastic fracture mechanics (LEFM) is based on a mathematical description of the near crack tip stress field developed by Irwin [23]. Consider a crack in an infinite plate with crack length 2a and a remotely applied tensile stress acting perpendicular to the crack plane (mode I). Irwin expressed the near crack tip stress field as a series solution ... 

K[ is the mode I stress intensity factor which serves as a scalar multiplier of the crack tip stress field. 

Fig. 2. Elastic solution for the crack tip stress field with. small scale yielding [24].

The utility of K or any elastic plastic fracture mechanics (EPFM) parameter to describe the mechanical driving force for crack growth is based on the ability of that parameter to characterize the stress-strain conditions at the crack tip in a maimer which accounts for a variety of crack lengths, component geometries and loading conditions. Equal values of K should correspond to equal crack tip stress-strain conditions and, consequently, to equivalent crack growth behavior. In such a case we have mechanical similitude. Mechanical similitude implies equivalent crack tip inelastic zones and equivalent elastic stress fields. Fracture mechanics is... 

The decrease in with crack depth for fracture of IG-11 graphite presents an interesting dilemma. The utihty of fracture mechanics is that equivalent values of K should represent an equivalent crack tip mechanical state and a singular critical value of K should define the failure criterion. Recall Eq. 2 where K is defined as the first term of the series solution for the crack tip stress field, Oy, normal to the crack plane. It was noted that this solution must be modified at the crack tip and at the far field. The maximum value of a. should be limited to and that the far... 

The decreasing value of K with decreasing flaw size for fracture of IG-11 graphite suggests that the near crack tip failure criterion would be better expressed by combining the near crack tip stress intensification estimated by K with the far field applied stress, Sfraa(Eq. 28). Using simple superposition of the stress perpendicular... 

Fig. 15. Local crack tip stress versus crack depth for small flaw fracture tests on IG-11 graphite.

The second physical quantity of interest is, r t = 90 pm, the critical crack tip stress field dimension. Irwin s analysis of the crack tip process zone dimension for an elastic-perfectly plastic material began with the perfectly elastic crack tip stress field solution of Eq. 1 and allowed for stress redistribution to account for the fact that the near crack tip field would be limited to Oj . The net result of this analysis is that the crack tip inelastic zone was nearly twice that predicted by Eq. 3, such that... 

The above observations enable a qualitative relation, based upon the role of crack tip blunting, to be postulated between the fracture behaviour and the viscoelastic yield behaviour of the materials1 8- 44,45). The basis for this relationship is the idea that crack-tip blunting decreases the local crack tip stress concentration and thus higher applied loads are required to cause failure. 

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